Yes actually the doors of the TARDIS are rather unique to the rest of the exterior. This is because the TARDIS has the most control over the doors, in some belief of mine, so as to not let the wrong people in. The Doctor even mentions out of anxiety to Amy that the lock is kinda loose and sorta has a mind of its own, to say. The TARDIS didn’t “like” Clara so it kept it’s doors locked even when she tried to get in. The TARDIS is a very mysterious thing but very easy to understand and love. So those doors being closed could actually mean that the TARDIS knew the Doctor was leaving so ‘pop’ she wanted them closed so as to let no one in. Agree? Disagree?